CFT Zoo

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list_of_cfts [2026/03/05 15:55]
Ludo Fraser-Taliente 		list_of_cfts [2026/03/05 16:00] (current)
Ludo Fraser-Taliente [One dimension]
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 ====== List of CFTs ====== ====== List of CFTs ======
  
-Here is a list of CFTs. They are organized by dimension. Note that some CFTs, like the [[gaussian|gaussian theories]] and [[percolation|percolation]], can be defined in any number of dimensions.+Here is a list of CFTs. They are organized by dimension. Note that some CFTs, like the [[gaussian|gaussian theories]] and [[percolation|percolation]], can be defined in any number of dimensions. This allows their conformal data to be analytically continued between dimensions, connecting otherwise apparently different CFTs.
  
 Some special classes of CFTs: Some special classes of CFTs:
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 ===== One dimension ===== ===== One dimension =====
  
-In 1d, the conformal Ward identity $T_\mu{}^\mu = 0$ implies $T_{00} = H = 0$. Therefore quantum systems which truly respect conformal invariance are non-local (see [[https://arxiv.org/pdf/1105.1772.pdf|here]] for another argument). Nonetheless, there are a number of interesting models exhibiting conformal symmetry or near conformal symmetry in one dimension.+In 1d, the conformal Ward identity $T_\mu{}^\mu = 0$ implies $T_{00} = H = 0$. Therefore quantum systems which truly respect conformal invariance are [[list_of_cfts#nonlocal_cfts|nonlocal]] (see [[https://arxiv.org/pdf/1105.1772.pdf|here]] for another argument). Nonetheless, there are a number of interesting models exhibiting conformal symmetry or near conformal symmetry in one dimension.
  
 {{topic>1d}} {{topic>1d}}
Last modified: 2026/03/05 15:55
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